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3 years ago

The line with the equation 4/5x +1/3y=1 is graphed one the xy-plane. What is the x-coordinate of the x-intercept of the line?

Mathematics

1 answer:

leva [86]3 years ago

4 0

Answer:

x = 4/5

Step-by-step explanation:

The x-intercept looks like (x, 0); the coordinate 0 indicates that the point lies on the x-axis. If we start with 4/5x + 1/3 y= 1 and let y = 0, we will get an equation for the x-intercept:

(4/5)x + (1/3)(0) =1

Then 4/5x = 1, and (5/4)(4/5)x = (1)(4/5).

Thus, x = 4/5, and the x-intercept is (4/5, 0).

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10) The scale of a map is 1 inch represents 4 miles. How many miles does 0.5 inches represent?

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Step-by-step explanation:

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At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A

alexgriva [62]

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) = 128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) = 128°(0.989)^22.3 + 72 = 172°

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3 years ago

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Wh

viktelen [127]

Answer:

Radius of sphere is 3 units.

Step-by-step explanation:

Volume of sphere is given by $4/3 \pi r^3$

surface area of sphere is given by $4 \pi r^2$

where r is the radius of the sphere.

Given that

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.

we equate formula of Volume of sphere and surface area of sphere

assuming r as the radius.

thus,

$4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3$

Thus, radius of sphere is 3 units.

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